134

CHANGE OF VOLUME IN CRYSTALLIZING.

[76. in 1784 and 1785 with 12-inch iron shells, filled with water, and closed by wooden plugs, and exposed to a temperature of about - 28° C. (-184 F.). In one case the shell was split by the expansion of the freezing water, and a sheet of ice projected from the crack formed in consequence of the sudden relief of the pressure (175, note.) In another experiment the wooden plug was thrown more than a hundred yards, and a cylinder of ice 8 inches in length protruded from the hole. The most compact ice has a density of 0923: 1000 parts of water at o° C. become dilated on freezing to about 1083.* It is owing to the expansion which occurs at the moment of solidification in iron and in Newton's fusible metal, that they answer so admirably for castings. Other solids, however, present equally remarkable instances of contraction, of which mercury, lead, and gold are illustrations, and hence the unfitness of the two metals last mentioned for the purposes of casting or moulding.

According to the experiments of Kopp (Liebig's Annal. 1855, xciii. 129), all the under-mentioned substances contract on solidifying, and their expansion at the moment of fusion is the following:

Many solids expand with much greater rapidity near their melting point than at lower temperatures; this is particularly remarkable in the case of wax. Kopp also finds that many hydrated salts expand at the moment of fusion, as for example :

A similar phenomenon attends the melting of Rose's fusible metal (2 parts of bismuth, I part of tin, and I of lead), which on liquefying, between 203 and 209° (95° and 98° C.), expands

*Dufour found, as the result of 22 careful experiments, that the density of ice varied between o'914 and o'923, with a mean of o'917: Bunsen's recent experiments, conducted with great precautions, lead to the number o'91674 for the density of ice at 0° (Pogg. Ann. 1870, cxli. 1).

77.]

DISSECTION OF CRYSTALLINE MASSES.

135

155 per cent. Iodine, bromine, potassium, sodium, tin, and bismuth, also contract at the moment of solidification, and of course expand on liquefaction.

(77) Dissection of Crystalline Masses.-An interesting proof of the influence of mass upon cohesion is sometimes observed in the gradual conversion of small crystals left in the liquid into larger ones. In nickelous sulphate, for example, slight alternate elevations and depressions of temperature cause the alternate solution and recrystallization of part of the salt; the smaller crystals, which offer the largest surface in proportion to their mass, are most readily dissolved, and their solution crystallizes again upon the surface of the larger ones, which thus increase in size gradually, whilst the smaller ones entirely disappear. Sparingly soluble compounds, by prolonged digestion in an appropriate solution, may sometimes be obtained in crystals. Amorphous argentic chloride may be thus gradually converted into crystals if digested in weak hydrochloric acid in sealed tubes. Many naturally crystallized minerals have doubtless increased in bulk considerably since their first deposition by this continuous process of alternate solution and crystallization.

By the slow action of solution, crystalline structure may often be made visible where no trace of it was previously apparent, and a kind of dissection of the mass is thus effected, owing to the more powerful exertion of cohesion in certain directions; these directions vary with the particular crystalline form of the compound. These phenomena may be developed in a striking manner upon the surface of a sheet of tin plate, by gently warming the plate, and washing it over while hot with a little weak acid; the crystalline forms thus displayed constitute, when the surface has been varnished, the ornamented tin plate termed moirée métallique. A bar of nickel placed in dilute nitric acid becomes covered with tetrahedra, from the solution of the intervening uncrystallized portions of the metal; and the fibrous structure of the better kinds of iron may be strikingly exhibited by a similar treatment of the mass. In all these cases the action of the solvent must be very weak, otherwise the force of adhesion will act too uniformly the more slowly the solution takes place, the more clearly is this difference in the amount of cohesion in different directions of the solid manifested. Salts may be made to show the same kind of structure without having recourse to chemical solvents. A shapeless block of alum, when placed in a nearly saturated solution of the salt, becomes gradually embossed with portions of octohedra, so that its true crystalline structure is revealed to the eye. (Daniell, Quart. Journ. of Science, 1816, i. 24, and Roy. Inst. Journ. i. 1.) Tyndall has studied the dissection of ice, by which its crystalline structure is exhibited (175).

:

A remarkable molecular change sometimes takes place in bodies without their undergoing any alteration from the solid to the liquid state. Both brass and silver, for example, when first cast or wrought, possess considerable toughness, and neither of them has any apparent crystalline structure; by repeated heatings and coolings, however, they often become so brittle as to snap off upon the application of a very slight degree of force, and the surface of the fracture then exhibits a distinctly crystallized appearance. In the same way it is found that constant vibration, such as that to which the iron shafts of machinery and the axles of railway carriages are subjected, gradually destroys the fibrous character to which the iron is chiefly indebted for its toughness, and renders it crystalline and brittle. A similar change sometimes occurs in crystallized bodies in this way transparent prismatic crystals of nickel sulphate or of zinc seleniate, when exposed for a few minutes to the sun's rays, become opaque; they retain their form until touched, and then crumble down into a granular powder composed of octohedral particles. An alteration somewhat similar occurs in barley sugar,

:

136

STRUCTURE OF CRYSTALS.

[77.

which, when first made from melted sugar, is vitreous and transparent; but it gradually becomes crystalline, opaque, and brittle.

(78) Structure of Crystals: Cleavage.-By the careful application of mechanical force, crystalline form may be often revealed in a body which at first appears as a shapeless mass. If to an irregular fragment of Iceland spar, for example, we apply the edge of a knife, and tap it gently on the back with a hammer, we shall find that in certain positions the spar splits readily, leaving smooth surfaces, and that having once obtained such a surface, we may go on splitting the mineral in layers parallel to the surface. Upon applying the knife to the surface of a layer so detached, we find that this layer admits of cleavage in two directions, so that ultimately a rhombohedral crystal is obtained from the spar. Some bodies admit of cleavage with much greater facility than others; and very often cleavage occurs more readily in the direction of one of the planes than in that of the others. Selenite, one of the forms of calcic sulphate, has three cleavages, but one of these is much more easily effected than the others; hence the mineral is readily split into laminæ.

Crystals are bounded by flat surfaces termed the faces or planes of the crystal (such as p p, fig. 50, 1). The lines,

angle. These planes are said to be similar, when their corresponding edges are proportional, and their corresponding angles equal. Edges are similar, when they are produced by the meeting of planes respectively similar, at equal angles; and angles are similar, when they are equal, and are contained within edges respectively similar. Sometimes it happens that the crystal is bounded in all directions by perfectly equal and similar faces, as is seen in the cube, the octohedron, and the rhombohedron. Such forms are distinguished as simple forms; whilst those forms resulting from the combination of two or more simple ones are termed compound or secondary forms. A crystal of quartz, consisting of a six-sided prism, terminated by two six-sided pyramids (fig. 51), is a compound form. In fig. 50, 2 is a compound form,

the twelve edges of the octohedron, d d d, being replaced by faces of the rhombic dodecahedron.

Although each substance has its own peculiar crystalline form, as, for example, alum the octohedron, common salt the cube, calcic carbonate the rhombohedron, it frequently happens that the regularity of the crystalline form is interfered with. Extra faces are often formed by the replacement of an edge, or the truncation of an angle. If the twelve solid edges of the octohedron were removed, a form intermediate

FIG. 51.

137

between the octohedron and the rhombic dodecahedron would be the result, such as is seen in fig. 50, 2. If the four solid angles of the tetrahedron were removed, a form intermediate between the tetrahedron and the octohedron would be obtained (fig. 50, 3).

In the discovery of the simple form of crystals, the process of cleavage just alluded to is most valuable; and by its means, secondary forms, which at first sight present no resemblance to the original, may be readily traced to it. A striking instance of this kind is afforded by the cleavage of the six-sided prism of calcareous spar. By cleavage, the three alternate edges of the base may be removed, and three faces produced, as at rr, fig. 52, whilst a cleavage similar to that of the base may be effected upon the opposite extremity of the prism, except that the edges corresponding to those that before resisted, now yield, and that those which at the base yielded to cleavage now remain entire. The obtuse rhombohedron is thus obtained by pursuing the dissection, as shown in fig. 52.

FIG. 52.

(79) Goniometers.-Since the number of geometrical solids is limited, whilst the number of crystallized bodies is very great, it necessarily happens that several different substances, possess the same crystalline form, and the only difference observable between them consists in the different inclination of the planes to each other; or, what is the same thing, in variations of the angles of the crystal. In order to detect this difference, the crystallographer requires instruments for measuring these angles. Such instruments are termed goniometers (from ywvía, an angle). Of these the simplest consists of a pair of double compasses, the pivot of which coincides with the centre of a graduated semicircle; one limb is fixed, forming the diameter of the semicircle, the other is movable on the pivot, and crosses the fixed limb at its

138

WOLLASTON'S REFLECTING GONIOMETER.

[79.

centre, as shown in fig. 53. The external limbs of the compasses are pressed against the two planes of the crystal, the incli

FIG. 53.

90

10

nation of which is to be measured, so that they shall accurately touch those planes in directions perpendicular to the edge at which they meet; and the alternate and opposite angle, which of course coincides with that of the crystal, is read off in the degrees of the graduated arc.

(80) Reflecting Goniometer.

-A far more elegant and accurate instrument is the reflecting goniometer of Wollaston, fig. 55.

FIG. 54.

The principle upon which it acts may be thus explained :-Let a b c d (fig. 54), represent a section of the crystal to be measured. A ray of light, i r, reflected as at rs, from the surface of the crystal, forms the radius of the arc which is to be measured. One plane, a b, of the crystal is brought into a fixed position with regard to the graduated circle, and the inclination of the two planes, a b, b c, is ascertained by measuring the arc which the graduated limb of the instrument describes, in order to bring the second plane, bc, of the crystal

into the same position as the first, a b. The supplement, a b c, of this arc, E c, measures the inclination of the two planes. The angle may, however, be read off at once, by attending to the following instructions:

The instrument (fig. 55) consists of a brass disk, a b, supported in a vertical plane, and graduated on its outer edge to half degrees. By means of a milled head, d, this disk may be turned round in its own plane; the angle through which it has been made to turn is read off by a vernier, c, which is permanently fixed. The axis, f, of the graduated circle is pierced by a second axis, attached to the milled head, e, which is intended to give